Question: ${4 \div \dfrac{5}{9} =}$
${4} \div \dfrac{5}{9}} ={\dfrac{4}{1}} \div \dfrac{5}{9}} $ $~~~~~~~{\gray{\text{Rewrite 4 as }\dfrac{4}{1}}}. $ $\phantom{4 \div \dfrac{2}{3}}} ={\dfrac{4}{1}} \times \dfrac{9}{5}}$ $ ~~~~~~{\gray{\text{Multiply by reciprocal of }\dfrac{5}{9}.}} $ $\phantom{8 \div \dfrac{2}{3}}} ={\dfrac{{4}\times9}}{1\timesD5}} $ $~~~~~~~{\gray{\text{Multiply. }}} $ $\phantom{8 \div \dfrac{2}{3}}} ={\dfrac{36}{5}} $ ${4 \div \dfrac{5}{9} =\dfrac{36}{5}}$ [Wait, can we rewrite the answer as a mixed number?]